Local regularity for texture segmentation: Combining wavelet leaders and proximal minimization

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

“…Wavelet coefficients are the most popular multiscale representation used to perform fractal analysis. Yet, it has recently been shown that, in the context of multifractal analysis and thus of local regularity estimation, wavelet coefficients are significantly outperformed by wavelet leaders, consisting of local suprema of wavelet coefficients [26][27][28][29]. While the methods proposed in the present contribution could be used with any multiscale representation, reported and discussed results are thus explicitly obtained using wavelet leaders.…”

“…In the present contribution, the estimation of the Hölder exponent is only performed using wavelet leaders L (γ) f (j, k), as preliminary contributions [27][28][29]32] report that wavelet leader based estimation outperforms those based on other multiresolution quantities. To indicate that the estimation of h and the segmentation procedures proposed in Section 3 below could be applied using any other multiresolution quantity, e.g., the modulus of the 2D-DWT coefficients, a generic notation X(j, k) is used instead of the specific L In the discrete setting, Hölder exponents are estimated for the locations x = 2k associated with the finest scale j = 1, and we make use of the notation · when we are dealing with matrices, rather than with matrix elements, e.g.,…”

“…Synthesis and analysis procedures will be made publicly available at the time of publication. Note that the present contribution significantly differs from the preliminary works [29,32] in that several methods involving TV are designed, and these methods are unified and compared on synthetic images and real-world textures.…”

“…In either case, the reliable and accurate detection and localization of actual changes in h is precluded. This explains why local regularity remains so far barely used for signal or texture characterization and segmentation (see, a contrario, [29][30][31][32][33]).…”

Review of wavelet‐based unsupervised texture segmentation, advantage of adaptive wavelets

“…Such approach allows for the definition of a global model through the local features which corresponds to characterize textures at different scales. Local regularity measured by either fractal dimension or local histogram on fuzzy regions (within a hierarchical framework to take into account different scales) was used to extract geometrical features in [6][7][8]. Because it corresponds to the human visual system, one of the most popular approach to extract texture features is based on Gabor wavelet filters [9][10][11][12][13][14].…”